Measurement exploratory data analysis

from tabulate import tabulate
from IPython.display import Markdown, HTML
import matplotlib.pylab as plt
from typing import List, Tuple

import pandas as pd
import numpy as np
from scipy.signal import find_peaks
from scipy.signal import butter, lfilter

from tsfel.feature_extraction.features import fundamental_frequency

import os
import sys
sys.path.append('../../')
from feature import mafaulda as src
from feature import discovery as fdiscovery

pd.set_option("display.notebook_repr_html", False)

Define data sources

DIR = '../../air_conditioning/'
file_list = [
    DIR + 'excool_digitalis/high_pressure_pump_40percent__1.tsv',
    DIR + 'excool_digitalis/high_pressure_pump_40percent__2.tsv',
    DIR + 'excool_digitalis/high_pressure_pump_40percent_speed_up__3.tsv',
    DIR + 'excool_digitalis/high_pressure_pump_80percent__4.tsv',
    DIR + 'shc2/compressor_shc2_klima4_bad.tsv',
    DIR + 'shc2/compressor_shc2_klima5_good.tsv',
    DIR + 'vertiv_digitalis/compressor_top_1.tsv',
    DIR + 'vertiv_digitalis/compressor_top_2.tsv',
    DIR + 'vertiv_digitalis/compressor_top_3.tsv',
    DIR + 'vertiv_digitalis/compressor_base.tsv',
    DIR + 'vertiv_digitalis/compressor_side.tsv'
]
Fs = 1160     # 1160 Hz +/-150 Hz (1020 - 1340 Hz)


file_list = [
    DIR + 'fan/speeds/1_still.tsv',
    DIR + 'fan/speeds/2_still.tsv',
    DIR + 'fan/speeds/3_still.tsv',
    DIR + 'fan/speeds/1_up.tsv',
    DIR + 'fan/speeds/2_up.tsv',
    DIR + 'fan/speeds/3_up.tsv',
    DIR + 'fan/speeds/1_down.tsv',
    DIR + 'fan/speeds/2_down.tsv',
    DIR + 'fan/speeds/3_down.tsv',
]
Fs = 2500

T_WAVEFORM = 5
T_SEC = T_WAVEFORM
NFFT = 1024

DATASET = []

Import dataset

for filename in file_list:
    ts = pd.read_csv(filename, delimiter='\t', index_col=False, header=None, names=['x', 'y', 'z'])
    # Calculate amplitude in m/s^2 Beaglebone Black ADC and ADXL335 resolution (VIN 1.8V, 12bits)
    for dim in ts.columns:
        ts[dim] = ts[dim] * (1800 / 4096)  # ADC to mV
        ts[dim] = (ts[dim] / 180) * 9.81  # mV to m/s^2 (180 mV/g)
        ts[dim] -= ts[dim].mean()

    ts['t'] = ts.index * (1 / Fs)
    ts.set_index('t', inplace=True)
    DATASET.append((os.path.basename(filename), ts))

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    ts.info()
    print()

1_still.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 38201 entries, 0.0 to 15.280000000000001
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       38201 non-null  float64
 1   y       38200 non-null  float64
 2   z       38200 non-null  float64
dtypes: float64(3)
memory usage: 1.2 MB

2_still.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 38201 entries, 0.0 to 15.280000000000001
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       38201 non-null  float64
 1   y       38200 non-null  float64
 2   z       38200 non-null  float64
dtypes: float64(3)
memory usage: 1.2 MB

3_still.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 38201 entries, 0.0 to 15.280000000000001
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       38201 non-null  float64
 1   y       38200 non-null  float64
 2   z       38200 non-null  float64
dtypes: float64(3)
memory usage: 1.2 MB

1_up.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 38201 entries, 0.0 to 15.280000000000001
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       38201 non-null  float64
 1   y       38200 non-null  float64
 2   z       38200 non-null  float64
dtypes: float64(3)
memory usage: 1.2 MB

2_up.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 38201 entries, 0.0 to 15.280000000000001
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       38201 non-null  float64
 1   y       38200 non-null  float64
 2   z       38200 non-null  float64
dtypes: float64(3)
memory usage: 1.2 MB

3_up.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 38201 entries, 0.0 to 15.280000000000001
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       38201 non-null  float64
 1   y       38200 non-null  float64
 2   z       38200 non-null  float64
dtypes: float64(3)
memory usage: 1.2 MB

1_down.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 38201 entries, 0.0 to 15.280000000000001
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       38201 non-null  float64
 1   y       38200 non-null  float64
 2   z       38200 non-null  float64
dtypes: float64(3)
memory usage: 1.2 MB

2_down.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 38201 entries, 0.0 to 15.280000000000001
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       38201 non-null  float64
 1   y       38200 non-null  float64
 2   z       38200 non-null  float64
dtypes: float64(3)
memory usage: 1.2 MB

3_down.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 38201 entries, 0.0 to 15.280000000000001
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       38201 non-null  float64
 1   y       38200 non-null  float64
 2   z       38200 non-null  float64
dtypes: float64(3)
memory usage: 1.2 MB

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    display(tabulate(ts.describe(), headers='keys', tablefmt='html'))

1_still.tsv

	x	y	z
count	38201	38200	38200
mean	-2.40499e-15	3.95579e-15	3.23185e-15
std	0.875637	1.2639	0.0920418
min	-9.07143	-2.52106	-0.348954
25%	-0.593063	-1.108	-0.061552
50%	0.0056921	-0.00628912	0.0102986
75%	0.580497	1.11937	0.058199
max	1.96961	2.43663	0.345601

2_still.tsv

	x	y	z
count	38201	38200	38200
mean	5.15893e-15	6.06082e-15	2.94447e-15
std	2.56549	2.48179	0.322518
min	-9.24575	-3.73282	-0.952338
25%	-2.44389	-2.63111	-0.281733
50%	0.430129	0.0752644	0.00566968
75%	2.27429	2.56608	0.269122
max	4.04661	3.66779	0.987628

3_still.tsv

	x	y	z
count	38201	38200	38200
mean	2.19072e-15	-3.27184e-16	1.05735e-14
std	2.15206	2.64354	0.396043
min	-9.32173	-4.12174	-0.786905
25%	-2.13667	-2.58893	-0.379752
50%	-0.244608	-0.0502045	0.00345146
75%	1.95881	2.56635	0.362704
max	3.92273	4.21293	0.841708

1_up.tsv

	x	y	z
count	38201	38200	38200
mean	7.1722e-16	1.16068e-15	-4.63229e-15
std	0.851834	1.19633	0.160765
min	-9.19537	-2.62078	-0.818255
25%	-0.381696	-0.704763	-0.0757992
50%	0.00150719	-0.010207	-0.00394865
75%	0.408661	0.756199	0.0679019
max	2.01332	2.57641	0.930109

2_up.tsv

	x	y	z
count	38201	38200	38200
mean	1.32693e-15	-5.37892e-15	3.77964e-16
std	2.54069	2.40738	0.506515
min	-9.66708	-4.29866	-1.69449
25%	-1.97907	-2.23894	-0.305381
50%	0.00879927	0.0123751	0.0778218
75%	1.99667	2.16789	0.341274
max	5.58919	4.61081	1.44298

3_up.tsv

	x	y	z
count	38201	38200	38200
mean	1.09015e-15	-3.60256e-15	1.23954e-15
std	1.69941	2.35114	0.38339
min	-9.81719	-4.07792	-0.81214
25%	-1.53042	-2.18586	-0.333137
50%	-0.0694594	0.0415091	0.00216618
75%	1.3436	2.10123	0.337469
max	3.93022	4.23279	1.12783

1_down.tsv

	x	y	z
count	38201	38200	38200
mean	6.07666e-15	-9.52239e-15	-2.13758e-15
std	0.276292	0.355092	0.0934928
min	-9.08741	-2.01469	-0.868043
25%	-0.0342404	-0.0268261	-0.0297866
50%	-0.0102902	-0.0028759	0.0181137
75%	0.01366	0.0210743	0.0420639
max	3.34274	2.05684	0.664769

2_down.tsv

	x	y	z
count	38201	38200	38200
mean	-3.53755e-15	4.22792e-16	2.48355e-15
std	0.911499	0.87873	0.242263
min	-9.16459	-3.82467	-1.76085
25%	-0.0156161	-0.0405354	-0.0124892
50%	0.00833407	0.007365	0.0354112
75%	0.0322843	0.0313152	0.0833116
max	4.89417	3.9352	1.56822

3_down.tsv

	x	y	z
count	38201	38200	38200
mean	3.38727e-15	-9.63697e-16	-5.49685e-15
std	0.676631	0.924902	0.236818
min	-9.08527	-3.8726	-3.24596
25%	-0.0321006	-0.0405711	-0.0126823
50%	0.0157998	0.00732926	0.0591683
75%	0.03975	0.0552297	0.0831185
max	3.77598	4.22256	7.81903

Time domain waveform

axis = ['x', 'y', 'z']
for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    
    ax = ts[axis].plot(figsize=(20, 8), grid=True, subplots=True)
    for i, axname in enumerate(axis):
        ax[i].set_xlabel('Time [s]')
        ax[i].set_ylabel(f'Amplitude ({axname}) [m/s^2]')
    plt.show()               # plt.savefig('waveform.png')

1_still.tsv

2_still.tsv

3_still.tsv

1_up.tsv

2_up.tsv

3_up.tsv

1_down.tsv

2_down.tsv

3_down.tsv

Time domain waveform zoom detail

axis = ['x', 'y', 'z']
for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    ax = (ts[axis].iloc[int(T_WAVEFORM*Fs):int(T_WAVEFORM*Fs)+Fs]
                  .plot(figsize=(20, 10), grid=True, subplots=True))
    
    for i, axname in enumerate(axis):
        ax[i].set_xlabel('Time [s]')
        ax[i].set_ylabel(f'Amplitude ({axname}) [m/s^2]')
        plt.show()      # plt.savefig('waveform_zoom.png')

1_still.tsv

2_still.tsv

3_still.tsv

1_up.tsv

2_up.tsv

3_up.tsv

1_down.tsv

2_down.tsv

3_down.tsv

def spectogram(x):
    fig, ax = plt.subplots(figsize=(15, 4))
    cmap = plt.get_cmap('inferno')
    pxx, freqs, t, im = plt.specgram(
        x, NFFT=NFFT, Fs=Fs,
        detrend='mean',
        mode='magnitude', scale='dB',
        cmap=cmap, vmin=-60
    )
    fig.colorbar(im, aspect=20, pad=0.04)
    ax.set_xlabel('Time [s]')
    ax.set_ylabel('Frequency [Hz]')
    src.resolution_calc(Fs, NFFT)
    return freqs, pxx

def window_idx(t):
    return (Fs * t) // NFFT + 1

def spectrum_slice(freqs, Pxx, t):
    fig, ax = plt.subplots(2, 1, figsize=(20, 8))
    n = window_idx(t)

    dB = 20 * np.log10(Pxx.T[n] / 0.000001)
    ax[0].plot(freqs, dB)      # 1 dB = 1 um/s^2
    ax[0].grid(True)
    ax[0].set_xlabel('Frequency [Hz]')
    ax[0].set_ylabel('Amplitude [dB]')
    
    ax[1].plot(freqs, Pxx.T[n])
    ax[1].grid(True)
    ax[1].set_xlabel('Frequency [Hz]')
    ax[1].set_ylabel('Amplitude [m/s^2]')
    return n


def get_max_frequency(freqs, Pxx, i):
    max_freq = freqs[np.argmax(Pxx.T[i])]
    return max_freq


def get_peaks(freqs, Pxx, i, top=5):
    amplitudes = Pxx.T[i]
    peaks, _ = find_peaks(amplitudes, distance=3)

    fundamental = get_max_frequency(freqs, Pxx, i)
    f_top = freqs[peaks[np.argsort(amplitudes[peaks])]][::-top]
    y_top = np.sort(amplitudes[peaks])[::-top]

    return pd.DataFrame({
        'f': f_top,
        'y': y_top,
        '1x': f_top / fundamental 
    })


def butter_bandpass_filter(data, lowcut, highcut, fs, order=5):
    b, a = butter(order, [lowcut, highcut], fs=fs, btype='band')
    y = lfilter(b, a, data)
    return y


def get_spectrograms(DATASET: List[pd.DataFrame], axis: str) -> list:
    spectrograms = []

    for name, ts in DATASET:
        base_freq = fundamental_frequency(ts[axis], Fs)
        display(Markdown(f'**{name}** *({axis.upper()} axis, Fundamental = {base_freq:.4f} Hz)*'))
        
        freqs, Pxx = spectogram(ts['x'])
        spectrograms.append((name, freqs, Pxx))
        plt.show()          # plt.savefig(f'x_axis_fft_{NFFT}.png')
    
    return spectrograms


def show_spectrogram_detail(spectrograms: list, axis: str, t: float):
    for name, freqs, Pxx in spectrograms:
        display(Markdown(f'**{name}** ({axis.upper()} axis @ {t}s)'))
        i_window = spectrum_slice(freqs, Pxx, t)
        # Incorrect fundamental frequency:
        # print(fdiscovery.harmonic_product_spectrum(freqs, Pxx.T[i_window]))
        plt.show()           #plt.savefig(f'x_axis_fft_{NFFT}_at_{T_SEC}s.png')


def show_mms_peaks(spectrograms: list, axis: str, t: float):
    for name, freqs, Pxx in spectrograms:
        display(Markdown(f'**{name}** ({axis.upper()} axis @ {t}s)'))
    
        i_window = window_idx(t)
        peaks = fdiscovery.mms_peak_finder(Pxx.T[i_window])
        
        fig, ax = plt.subplots(1, 1, figsize=(15, 3))
        ax.grid(True)
        ax.plot(freqs, Pxx.T[i_window])
        ax.scatter(freqs[peaks], Pxx.T[i_window][peaks], marker='^', color='red')
        ax.set_xlabel('Frequency [Hz]')
        
        plt.show()


def show_harmonic_series(spectrograms: list, axis: str, t: float):
    # https://stackoverflow.com/questions/1982770/changing-the-color-of-an-axis
    for name, freqs, Pxx in spectrograms:
        display(Markdown(f'**{name}** ({axis.upper()} axis @ {t}s)'))
    
        i_window = window_idx(t)
        h_series = fdiscovery.harmonic_series_detection(freqs, Pxx.T[i_window], Fs, NFFT)
    
        # Find best (sum of harmonics' amplitudes in the largest)
        max_harmonic_amp_idx = np.argmax([
            sum([h[1] for h in s]) / len(s)
            for s in h_series
        ])
        best_harmonic_series = pd.DataFrame(
            h_series[max_harmonic_amp_idx],
            columns=['Frequency [Hz]', 'Amplitude [m/s^2]']
        )
        best_harmonic_series.index += 1
        display(tabulate(best_harmonic_series, headers='keys', tablefmt='html'))
    
        # Plot found harmonic series
        fig, ax = plt.subplots(1, 8, figsize=(30, 4))
        for i in range(8):
            s = h_series[i+1]
            if i == max_harmonic_amp_idx:
                ax[i].xaxis.label.set_color('red')
    
            ax[i].plot(freqs, Pxx.T[i_window])
            ax[i].scatter([x[0] for x in s], [x[1] for x in s], marker='^', color='red')
            ax[i].set_xlabel('Frequency [Hz]')
    
        plt.show()

def show_spectra_largest_amplitudes(spectrograms: list, axis: str, t: float):
    for name, freqs, Pxx in spectrograms:
        display(Markdown(f'**{name}** ({axis.upper()} axis @ {t}s)'))

        i_window = window_idx(t)
        x_fundamental = get_max_frequency(freqs, Pxx, i_window)
        peaks = get_peaks(freqs, Pxx, i_window)
        
        display(Markdown(f'- *Fundamental frequency:* {x_fundamental} Hz'))
        display(tabulate(peaks.head(5), headers='keys', tablefmt='html'))

Spectrogram in X axis

x_spectra = get_spectrograms(DATASET, 'x')

1_still.tsv (X axis, Fundamental = 18.4550 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

2_still.tsv (X axis, Fundamental = 20.3529 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

3_still.tsv (X axis, Fundamental = 21.9890 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

1_up.tsv (X axis, Fundamental = 18.5205 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

2_up.tsv (X axis, Fundamental = 20.4183 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

3_up.tsv (X axis, Fundamental = 22.0544 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

1_down.tsv (X axis, Fundamental = 17.2116 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

2_down.tsv (X axis, Fundamental = 20.3529 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

3_down.tsv (X axis, Fundamental = 21.4000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

Spectrogram detail in X axis

show_spectrogram_detail(x_spectra, 'x', T_SEC)

1_still.tsv (X axis @ 5s)

2_still.tsv (X axis @ 5s)

3_still.tsv (X axis @ 5s)

1_up.tsv (X axis @ 5s)

2_up.tsv (X axis @ 5s)

3_up.tsv (X axis @ 5s)

1_down.tsv (X axis @ 5s)

2_down.tsv (X axis @ 5s)

3_down.tsv (X axis @ 5s)

Peaks in frequency spectrum in X axis

• MMS peak finder algorithm

show_mms_peaks(x_spectra, 'x', T_SEC)

1_still.tsv (X axis @ 5s)

2_still.tsv (X axis @ 5s)

3_still.tsv (X axis @ 5s)

1_up.tsv (X axis @ 5s)

2_up.tsv (X axis @ 5s)

3_up.tsv (X axis @ 5s)

1_down.tsv (X axis @ 5s)

2_down.tsv (X axis @ 5s)

3_down.tsv (X axis @ 5s)

Harmonic series detection in X axis

show_harmonic_series(x_spectra, 'x', T_SEC)

1_still.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	19.5312	0.546024
2	36.6211	0.0221022
3	56.1523	0.0854366
4	73.2422	0.00486936
5	92.7734	0.00363132
6	134.277	0.00462071
7	285.645	0.00223661
8	778.809	0.00111313

2_still.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	19.5312	1.60475
2	41.5039	0.476521
3	61.0352	0.128852
4	73.2422	0.00488967
5	134.277	0.00695457
6	229.492	0.0033906
7	437.012	0.00108532
8	1044.92	0.000367557

3_still.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	21.9727	1.49894
2	43.9453	0.252232
3	65.918	0.185653
4	87.8906	0.0101309
5	185.547	0.00249273
6	292.969	0.00785039
7	314.941	0.011506

1_up.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	17.0898	0.468103
2	36.6211	0.0218309
3	53.7109	0.300899
4	70.8008	0.0112762
5	136.719	0.00141639
6	205.078	0.00174178
7	458.984	0.000805989

2_up.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	19.5312	2.06101
2	41.5039	0.291134
3	61.0352	0.0746276
4	78.125	0.0223562
5	112.305	0.0122052
6	209.961	0.00244761
7	361.328	0.00291835
8	437.012	0.000683408

3_up.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	21.9727	1.00514
2	43.9453	0.206071
3	65.918	0.145704
4	87.8906	0.00827826
5	146.484	0.00109411
6	187.988	0.00169469
7	314.941	0.0100025

1_down.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	4.88281	0.00608786
2	9.76562	0.00201308
3	9.76562	0.00201308
4	17.0898	0.0147896
5	24.4141	0.00791007
6	31.7383	0.00874098
7	63.4766	0.00307372
8	288.086	0.000580757

2_down.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	4.88281	0.0179338
2	4.88281	0.0179338
3	12.207	0.00271084
4	19.5312	0.0323693
5	19.5312	0.0323693
6	26.8555	0.00722242
7	80.5664	0.00146388
8	144.043	0.0021425
9	520.02	0.000464282

3_down.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	4.88281	0.0178097
2	4.88281	0.0178097
3	21.9727	0.0823231
4	21.9727	0.0823231
5	31.7383	0.0157251
6	43.9453	0.0165751
7	100.098	0.0016314
8	375.977	0.000959079
9	895.996	0.000618653

show_spectra_largest_amplitudes(x_spectra, 'x', T_SEC)

1_still.tsv (X axis @ 5s)

• Fundamental frequency: 19.53125 Hz

	f	y	1x
0	19.5312	0.546024	1
1	195.312	0.00964576	10
2	134.277	0.00462071	6.875
3	214.844	0.00275034	11
4	412.598	0.00243231	21.125

2_still.tsv (X axis @ 5s)

• Fundamental frequency: 19.53125 Hz

	f	y	1x
0	19.5312	1.60475	1
1	51.2695	0.0283099	2.625
2	195.312	0.010183	10
3	273.438	0.00566994	14
4	332.031	0.00470596	17

3_still.tsv (X axis @ 5s)

• Fundamental frequency: 21.97265625 Hz

	f	y	1x
0	21.9727	1.49894	1
1	314.941	0.011506	14.3333
2	329.59	0.00853408	15
3	97.6562	0.00731069	4.44444
4	9.76562	0.00419778	0.444444

1_up.tsv (X axis @ 5s)

• Fundamental frequency: 17.08984375 Hz

	f	y	1x
0	17.0898	0.468103	1
1	70.8008	0.0112762	4.14286
2	295.41	0.00670006	17.2857
3	144.043	0.00419564	8.42857
4	87.8906	0.00272608	5.14286

2_up.tsv (X axis @ 5s)

• Fundamental frequency: 19.53125 Hz

	f	y	1x
0	19.5312	2.06101	1
1	78.125	0.0223562	4
2	178.223	0.00997867	9.125
3	307.617	0.00613189	15.75
4	314.941	0.00486118	16.125

3_up.tsv (X axis @ 5s)

• Fundamental frequency: 21.97265625 Hz

	f	y	1x
0	21.9727	1.00514	1
1	195.312	0.0102214	8.88889
2	292.969	0.00891474	13.3333
3	12.207	0.00589523	0.555556
4	163.574	0.00447052	7.44444

1_down.tsv (X axis @ 5s)

• Fundamental frequency: 17.08984375 Hz

	f	y	1x
0	17.0898	0.0147896	1
1	53.7109	0.00494662	3.14286
2	205.078	0.00197908	12
3	83.0078	0.00169884	4.85714
4	173.34	0.00152013	10.1429

2_down.tsv (X axis @ 5s)

• Fundamental frequency: 19.53125 Hz

	f	y	1x
0	19.5312	0.0323693	1
1	48.8281	0.00282413	2.5
2	163.574	0.00189572	8.375
3	361.328	0.00152447	18.5
4	80.5664	0.00146388	4.125

3_down.tsv (X axis @ 5s)

• Fundamental frequency: 21.97265625 Hz

	f	y	1x
0	21.9727	0.0823231	1
1	65.918	0.006334	3
2	190.43	0.00178213	8.66667
3	339.355	0.00146555	15.4444
4	283.203	0.00120351	12.8889

Spectrogram in Y axis

y_spectra = get_spectrograms(DATASET, 'y')

1_still.tsv (Y axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

2_still.tsv (Y axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

3_still.tsv (Y axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

1_up.tsv (Y axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

2_up.tsv (Y axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

3_up.tsv (Y axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

1_down.tsv (Y axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

2_down.tsv (Y axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

3_down.tsv (Y axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

Spectrogram detail in Y axis

show_spectrogram_detail(y_spectra, 'y', T_SEC)

1_still.tsv (Y axis @ 5s)

2_still.tsv (Y axis @ 5s)

3_still.tsv (Y axis @ 5s)

1_up.tsv (Y axis @ 5s)

2_up.tsv (Y axis @ 5s)

3_up.tsv (Y axis @ 5s)

1_down.tsv (Y axis @ 5s)

2_down.tsv (Y axis @ 5s)

3_down.tsv (Y axis @ 5s)

Peaks in frequency spectrum in Y axis

show_mms_peaks(y_spectra, 'y', T_SEC)

1_still.tsv (Y axis @ 5s)

2_still.tsv (Y axis @ 5s)

3_still.tsv (Y axis @ 5s)

1_up.tsv (Y axis @ 5s)

2_up.tsv (Y axis @ 5s)

3_up.tsv (Y axis @ 5s)

1_down.tsv (Y axis @ 5s)

2_down.tsv (Y axis @ 5s)

3_down.tsv (Y axis @ 5s)

Harmonic series detection in Y axis

show_harmonic_series(y_spectra, 'y', T_SEC)

1_still.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	19.5312	0.546024
2	36.6211	0.0221022
3	56.1523	0.0854366
4	73.2422	0.00486936
5	92.7734	0.00363132
6	134.277	0.00462071
7	285.645	0.00223661
8	778.809	0.00111313

2_still.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	19.5312	1.60475
2	41.5039	0.476521
3	61.0352	0.128852
4	73.2422	0.00488967
5	134.277	0.00695457
6	229.492	0.0033906
7	437.012	0.00108532
8	1044.92	0.000367557

3_still.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	21.9727	1.49894
2	43.9453	0.252232
3	65.918	0.185653
4	87.8906	0.0101309
5	185.547	0.00249273
6	292.969	0.00785039
7	314.941	0.011506

1_up.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	17.0898	0.468103
2	36.6211	0.0218309
3	53.7109	0.300899
4	70.8008	0.0112762
5	136.719	0.00141639
6	205.078	0.00174178
7	458.984	0.000805989

2_up.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	19.5312	2.06101
2	41.5039	0.291134
3	61.0352	0.0746276
4	78.125	0.0223562
5	112.305	0.0122052
6	209.961	0.00244761
7	361.328	0.00291835
8	437.012	0.000683408

3_up.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	21.9727	1.00514
2	43.9453	0.206071
3	65.918	0.145704
4	87.8906	0.00827826
5	146.484	0.00109411
6	187.988	0.00169469
7	314.941	0.0100025

1_down.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	4.88281	0.00608786
2	9.76562	0.00201308
3	9.76562	0.00201308
4	17.0898	0.0147896
5	24.4141	0.00791007
6	31.7383	0.00874098
7	63.4766	0.00307372
8	288.086	0.000580757

2_down.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	4.88281	0.0179338
2	4.88281	0.0179338
3	12.207	0.00271084
4	19.5312	0.0323693
5	19.5312	0.0323693
6	26.8555	0.00722242
7	80.5664	0.00146388
8	144.043	0.0021425
9	520.02	0.000464282

3_down.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	4.88281	0.0178097
2	4.88281	0.0178097
3	21.9727	0.0823231
4	21.9727	0.0823231
5	31.7383	0.0157251
6	43.9453	0.0165751
7	100.098	0.0016314
8	375.977	0.000959079
9	895.996	0.000618653

show_spectra_largest_amplitudes(y_spectra, 'y', T_SEC)

1_still.tsv (Y axis @ 5s)

• Fundamental frequency: 19.53125 Hz

	f	y	1x
0	19.5312	0.546024	1
1	195.312	0.00964576	10
2	134.277	0.00462071	6.875
3	214.844	0.00275034	11
4	412.598	0.00243231	21.125

2_still.tsv (Y axis @ 5s)

• Fundamental frequency: 19.53125 Hz

	f	y	1x
0	19.5312	1.60475	1
1	51.2695	0.0283099	2.625
2	195.312	0.010183	10
3	273.438	0.00566994	14
4	332.031	0.00470596	17

3_still.tsv (Y axis @ 5s)

• Fundamental frequency: 21.97265625 Hz

	f	y	1x
0	21.9727	1.49894	1
1	314.941	0.011506	14.3333
2	329.59	0.00853408	15
3	97.6562	0.00731069	4.44444
4	9.76562	0.00419778	0.444444

1_up.tsv (Y axis @ 5s)

• Fundamental frequency: 17.08984375 Hz

	f	y	1x
0	17.0898	0.468103	1
1	70.8008	0.0112762	4.14286
2	295.41	0.00670006	17.2857
3	144.043	0.00419564	8.42857
4	87.8906	0.00272608	5.14286

2_up.tsv (Y axis @ 5s)

• Fundamental frequency: 19.53125 Hz

	f	y	1x
0	19.5312	2.06101	1
1	78.125	0.0223562	4
2	178.223	0.00997867	9.125
3	307.617	0.00613189	15.75
4	314.941	0.00486118	16.125

3_up.tsv (Y axis @ 5s)

• Fundamental frequency: 21.97265625 Hz

	f	y	1x
0	21.9727	1.00514	1
1	195.312	0.0102214	8.88889
2	292.969	0.00891474	13.3333
3	12.207	0.00589523	0.555556
4	163.574	0.00447052	7.44444

1_down.tsv (Y axis @ 5s)

• Fundamental frequency: 17.08984375 Hz

	f	y	1x
0	17.0898	0.0147896	1
1	53.7109	0.00494662	3.14286
2	205.078	0.00197908	12
3	83.0078	0.00169884	4.85714
4	173.34	0.00152013	10.1429

2_down.tsv (Y axis @ 5s)

• Fundamental frequency: 19.53125 Hz

	f	y	1x
0	19.5312	0.0323693	1
1	48.8281	0.00282413	2.5
2	163.574	0.00189572	8.375
3	361.328	0.00152447	18.5
4	80.5664	0.00146388	4.125

3_down.tsv (Y axis @ 5s)

• Fundamental frequency: 21.97265625 Hz

	f	y	1x
0	21.9727	0.0823231	1
1	65.918	0.006334	3
2	190.43	0.00178213	8.66667
3	339.355	0.00146555	15.4444
4	283.203	0.00120351	12.8889

Spectrogram in Z axis

z_spectra = get_spectrograms(DATASET, 'z')

1_still.tsv (Z axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

2_still.tsv (Z axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

3_still.tsv (Z axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

1_up.tsv (Z axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

2_up.tsv (Z axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

3_up.tsv (Z axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

1_down.tsv (Z axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

2_down.tsv (Z axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

3_down.tsv (Z axis, Fundamental = 0.0000 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

Spectrogram detail in Z axis

show_spectrogram_detail(z_spectra, 'z', T_SEC)

1_still.tsv (Z axis @ 5s)

2_still.tsv (Z axis @ 5s)

3_still.tsv (Z axis @ 5s)

1_up.tsv (Z axis @ 5s)

2_up.tsv (Z axis @ 5s)

3_up.tsv (Z axis @ 5s)

1_down.tsv (Z axis @ 5s)

2_down.tsv (Z axis @ 5s)

3_down.tsv (Z axis @ 5s)

Peaks in frequency spectrum in Z axis

show_mms_peaks(z_spectra, 'z', T_SEC)

1_still.tsv (Z axis @ 5s)

2_still.tsv (Z axis @ 5s)

3_still.tsv (Z axis @ 5s)

1_up.tsv (Z axis @ 5s)

2_up.tsv (Z axis @ 5s)

3_up.tsv (Z axis @ 5s)

1_down.tsv (Z axis @ 5s)

2_down.tsv (Z axis @ 5s)

3_down.tsv (Z axis @ 5s)

Harmonic series detection in Z axis

show_harmonic_series(z_spectra, 'z', T_SEC)

1_still.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	19.5312	0.546024
2	36.6211	0.0221022
3	56.1523	0.0854366
4	73.2422	0.00486936
5	92.7734	0.00363132
6	134.277	0.00462071
7	285.645	0.00223661
8	778.809	0.00111313

2_still.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	19.5312	1.60475
2	41.5039	0.476521
3	61.0352	0.128852
4	73.2422	0.00488967
5	134.277	0.00695457
6	229.492	0.0033906
7	437.012	0.00108532
8	1044.92	0.000367557

3_still.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	21.9727	1.49894
2	43.9453	0.252232
3	65.918	0.185653
4	87.8906	0.0101309
5	185.547	0.00249273
6	292.969	0.00785039
7	314.941	0.011506

1_up.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	17.0898	0.468103
2	36.6211	0.0218309
3	53.7109	0.300899
4	70.8008	0.0112762
5	136.719	0.00141639
6	205.078	0.00174178
7	458.984	0.000805989

2_up.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	19.5312	2.06101
2	41.5039	0.291134
3	61.0352	0.0746276
4	78.125	0.0223562
5	112.305	0.0122052
6	209.961	0.00244761
7	361.328	0.00291835
8	437.012	0.000683408

3_up.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	21.9727	1.00514
2	43.9453	0.206071
3	65.918	0.145704
4	87.8906	0.00827826
5	146.484	0.00109411
6	187.988	0.00169469
7	314.941	0.0100025

1_down.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	4.88281	0.00608786
2	9.76562	0.00201308
3	9.76562	0.00201308
4	17.0898	0.0147896
5	24.4141	0.00791007
6	31.7383	0.00874098
7	63.4766	0.00307372
8	288.086	0.000580757

2_down.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	4.88281	0.0179338
2	4.88281	0.0179338
3	12.207	0.00271084
4	19.5312	0.0323693
5	19.5312	0.0323693
6	26.8555	0.00722242
7	80.5664	0.00146388
8	144.043	0.0021425
9	520.02	0.000464282

3_down.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	4.88281	0.0178097
2	4.88281	0.0178097
3	21.9727	0.0823231
4	21.9727	0.0823231
5	31.7383	0.0157251
6	43.9453	0.0165751
7	100.098	0.0016314
8	375.977	0.000959079
9	895.996	0.000618653

show_spectra_largest_amplitudes(z_spectra, 'z', T_SEC)

1_still.tsv (Z axis @ 5s)

• Fundamental frequency: 19.53125 Hz

	f	y	1x
0	19.5312	0.546024	1
1	195.312	0.00964576	10
2	134.277	0.00462071	6.875
3	214.844	0.00275034	11
4	412.598	0.00243231	21.125

2_still.tsv (Z axis @ 5s)

• Fundamental frequency: 19.53125 Hz

	f	y	1x
0	19.5312	1.60475	1
1	51.2695	0.0283099	2.625
2	195.312	0.010183	10
3	273.438	0.00566994	14
4	332.031	0.00470596	17

3_still.tsv (Z axis @ 5s)

• Fundamental frequency: 21.97265625 Hz

	f	y	1x
0	21.9727	1.49894	1
1	314.941	0.011506	14.3333
2	329.59	0.00853408	15
3	97.6562	0.00731069	4.44444
4	9.76562	0.00419778	0.444444

1_up.tsv (Z axis @ 5s)

• Fundamental frequency: 17.08984375 Hz

	f	y	1x
0	17.0898	0.468103	1
1	70.8008	0.0112762	4.14286
2	295.41	0.00670006	17.2857
3	144.043	0.00419564	8.42857
4	87.8906	0.00272608	5.14286

2_up.tsv (Z axis @ 5s)

• Fundamental frequency: 19.53125 Hz

	f	y	1x
0	19.5312	2.06101	1
1	78.125	0.0223562	4
2	178.223	0.00997867	9.125
3	307.617	0.00613189	15.75
4	314.941	0.00486118	16.125

3_up.tsv (Z axis @ 5s)

• Fundamental frequency: 21.97265625 Hz

	f	y	1x
0	21.9727	1.00514	1
1	195.312	0.0102214	8.88889
2	292.969	0.00891474	13.3333
3	12.207	0.00589523	0.555556
4	163.574	0.00447052	7.44444

1_down.tsv (Z axis @ 5s)

• Fundamental frequency: 17.08984375 Hz

	f	y	1x
0	17.0898	0.0147896	1
1	53.7109	0.00494662	3.14286
2	205.078	0.00197908	12
3	83.0078	0.00169884	4.85714
4	173.34	0.00152013	10.1429

2_down.tsv (Z axis @ 5s)

• Fundamental frequency: 19.53125 Hz

	f	y	1x
0	19.5312	0.0323693	1
1	48.8281	0.00282413	2.5
2	163.574	0.00189572	8.375
3	361.328	0.00152447	18.5
4	80.5664	0.00146388	4.125

3_down.tsv (Z axis @ 5s)

• Fundamental frequency: 21.97265625 Hz

	f	y	1x
0	21.9727	0.0823231	1
1	65.918	0.006334	3
2	190.43	0.00178213	8.66667
3	339.355	0.00146555	15.4444
4	283.203	0.00120351	12.8889

Histogram

axis = ['x', 'y', 'z']
for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    ts[axis].hist(figsize=(10, 5), grid=True, bins=50)
    plt.show()

1_still.tsv

2_still.tsv

3_still.tsv

1_up.tsv

2_up.tsv

3_up.tsv

1_down.tsv

2_down.tsv

3_down.tsv

Orbitals of all cross sections

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    fig, ax = plt.subplots(1, 3, figsize=(20, 4))

    for i, col in enumerate([('x', 'y'), ('x', 'z'), ('y', 'z')]):
        ax[i].scatter(ts[col[0]], ts[col[1]], s=1)
        ax[i].grid(True)
        ax[i].set_xlabel(col[0].upper())
        ax[i].set_ylabel(col[1].upper())
        ax[i].grid(True)
    plt.show()       # plt.savefig('orbitals.png')

1_still.tsv

2_still.tsv

3_still.tsv

1_up.tsv

2_up.tsv

3_up.tsv

1_down.tsv

2_down.tsv

3_down.tsv

Orbitals of 1x harmonic frequency

x_spectra_by_name = {spec[0]: spec for spec in x_spectra}
y_spectra_by_name = {spec[0]: spec for spec in y_spectra}
z_spectra_by_name = {spec[0]: spec for spec in z_spectra}
t = 5
space = 5

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    fig, ax = plt.subplots(1, 3, figsize=(20, 4))

    name, freqs, Pxx = x_spectra_by_name[name]
    x_fundamental = get_max_frequency(freqs, Pxx, window_idx(t))

    name, freqs, Pxx = y_spectra_by_name[name]
    y_fundamental = get_max_frequency(freqs, Pxx, window_idx(t))

    name, freqs, Pxx = z_spectra_by_name[name]
    z_fundamental = get_max_frequency(freqs, Pxx, window_idx(t))

    ts['x_1x'] = butter_bandpass_filter(ts['x'], x_fundamental - space, x_fundamental + space, Fs)
    ts['y_1x'] = butter_bandpass_filter(ts['y'], y_fundamental - space, y_fundamental + space, Fs)
    ts['z_1x'] = butter_bandpass_filter(ts['z'], z_fundamental - space, z_fundamental + space, Fs)
    
    for i, col in enumerate([('x_1x', 'y_1x'), ('x_1x', 'z_1x'), ('y_1x', 'z_1x')]):
        ax[i].scatter(ts[col[0]], ts[col[1]], s=1)
        ax[i].grid(True)
        ax[i].set_xlabel(col[0].upper())
        ax[i].set_ylabel(col[1].upper())
        ax[i].grid(True)
    
    plt.show()       # plt.savefig('orbitals_1x.png')

1_still.tsv

2_still.tsv

3_still.tsv

1_up.tsv

2_up.tsv

3_up.tsv

1_down.tsv

2_down.tsv

3_down.tsv